Potential energy surface reaction coordinate diagram

Fig. 7. Energetics of a bimolecular rate process. Top Representation of the potential energy surface along coordinate axes corresponding to the interatomic distance of B-to-C and A-to-B, where incremental displacements along the potential energy axis are shown as a series of isoenergetic lines (each marked by arbitrarily chosen numbers to indicate increased energy of the transition-state (TS) intermediate relative to the reactants). Bottom Typical reaction coordinate diagram for a bimolecular group transfer reaction.

The potential energy surface consists of two valleys separated by a col or saddle. The reacting system will tend to follow a path of minimum potential energy in its progress from the initial state of reactants (A + BC) to the final state of products (AB -F C). This path is indicated by the dashed line from reactants to products in Fig. 5-2. This path is called the reaction coordinate, and a plot of potential energy as a function of the reaction coordinate is called a reaction coordinate diagram. 

Figure 5-3. Reaction coordinate diagram for the potential energy surface of Fig. 5-2.

Let us now turn to the surfaces themselves to learn the kinds of kinetic information they contain. First observe that the potential energy surface of Fig. 5-2 is drawn to be symmetrical about the 45° diagonal. This is the type of surface to be expected for a symmetrical reaction like H -I- H2 = H2 -h H, in which the reactants and products are identical. The corresponding reaction coordinate diagram in Fig. 5-3, therefore, shows the reactants and products having the same stability (energy) and the transition state appearing at precisely the midpoint of the reaction coordinate. 

Fig. 5. Potential energy-reaction coordinate diagram for an electron transfer reaction leading to a product adsorbed on the electrode surface.

Figure 2.4. Reaction coordinate diagram for a simple chemical reaction. The reactant A is converted to product B. The R curve represents the potential energy surface of the reactant and the P curve the potential energy surface of the product. Thermal activation leads to an over-the-barrier process at transition state X. The vibrational states have been shown for the reactant A. As temperature increases, the higher energy vibrational states are occupied leading to increased penetration of the P curve below the classical transition state, and therefore increased tunnelling probability.

A depiction of a hypothetical potential energy surface for a reacting system as a function of two chosen coordinates (c.g., the lengths of two bonds being broken). Such diagrams are useful in assessing structural effects on transition states for stepwise or concerted pathways. An example of More O Ferrall-Jencks diagrams for j8-elimina-tion reactions is shown below. 

Graphical representation of the saddle point (here marked with an X) for the transfer of atom B as the substance A-B reacts with another species, C. Potential energy is plotted in the vertical direction. Note also that the surface resembles a horse saddle, with the horn of the saddle closest to the observer. As drawn here, the dissociation to form three discrete species (A + B J- C) requires much more energy than that needed to surmount the path that includes the saddle point. A two-dimensional "slice" through a saddle point diagram is typically called a reaction-coordinate diagram or potential-energy profile. 

Free energy diagrams for enzymes REACTION COORDINATE DIAGRAM ENZYME ENERGETICS POTENTIAL-ENERGY SURFACES TRANSITION-STATE THEORY ARRHENIUS EQUATION VAN T HOFF RELATIONSHIP... 

Fig. 9.17. Schematic diagram of the potential energy surfaces for an electron transfer reaction the generalized coordinates xand y correspond to inner and outer sphere modes, respectively. (Reprinted from R. J. D. Miller, G. L. McLendon, A. J. Nozik, W. Schnickle, and F. Willig, Surface Electron Transfer Processes, p. 58, copyright 1995 VCH-Wiley. Reprinted by permission of John Wiley Sons, Inc.)...

For further discussion of three-dimensional reaction coordinate diagrams for these processes, see Section 5.4, p. 246, and (a) W. P. Jencks, Chem. Rev., 72, 705 (1972). (b) M. Choi and E. R. Thornton, J. Amer. Chem. Soc., 96, 1428 (1974), have suggested the possibility of more complex reaction paths with two consecutive transition states not separated by any energy minimum and with reaction coordinates perpendicular to each other on the potential energy surface. 

In terms of a potential energy surface, attractive release occurs in the valley of the reactants, as judged from the energy contours, repulsive release in that of the products, and mixed in the transition region. These concepts are illustrated in the reaction coordinate diagram, Fig. 1. 

Fig. 2.7 The ozone/isoozone potential energy surface (calculated by the AMI method Chapter 6), a 2D surface in a 3D diagram. The dashed line on the surface is the reaction coordinate (intrinsic reaction coordinate, IRC). A slice through the reaction coordinate gives a ID surface in a 2D diagram. The diagram is not meant to be quantitatively accurate...

To predict the shape of potential energy surfaces along the symmetry-retaining reaction coordinate from an MO correlation diagram, one must construct a correlation diagram of the electronic configurations (Figure 4.35). 

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